Nuprl Lemma : geo-colinear-not-out
∀e:BasicGeometry. ∀a,b,c:Point. (Colinear(a;b;c) ⇒ (¬out(a bc) ⇐⇒ B(bac)))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
geo-between: B(abc),
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
false: False,
prop: ℙ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
stable: Stable{P},
euclidean-plane: EuclideanPlane,
basic-geometry: BasicGeometry,
or: P ∨ Q,
geo-eq: a ≡ b,
geo-out: out(p ab),
cand: A c∧ B,
basic-geometry-: BasicGeometry-
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. (Colinear(a;b;c) {}\mRightarrow{} (\mneg{}out(a bc) \mLeftarrow{}{}\mRightarrow{} B(bac)))
Date html generated:
2020_05_20-AM-09_55_39
Last ObjectModification:
2019_12_23-AM-10_13_59
Theory : euclidean!plane!geometry
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